Project Cyclops, A Design... - Department of Earth and Planetary ...

lO II
Substituting this relation into equation 5, Chapter 5,
with Po = fiB we find the conventional range limit
o
t---
iv.
10 to
w 109
._1
R
- 4 _'-B I (9)
q__ dr t1_)1/2 n I]4, n >> I (10)
m
er
u_ 108
0
¢Y
w
en
z
107
where
dr = receiving antenna diameter
Peff = Ptgt = effective radiated power
= noise spectral density = kTat radio frequencies
B = receiver bandwidth
10 6
I01
10 2 I0 3 I0 4 I0 5
ANTENNA
DIAMETER
r = integration time
n = (Br)
Figure 6-4.
Number of resolvable directions versus
diameter
SEARCH RANGE LIMIT
and wavelength.
in radio astronomy and in most fields of measurement
the minimum detectable signal amplitude is defined
as being equal to the rms fluctuations due to noise.
The signal-to-noise power ratio out of a square-law
detector is given by equation (19) in Chapter 5 as
where
Pr = received signal power
Po = noise power
s ('°r/t'o)2
--= n (7)
N 1 + 2(Pr/Po)
n = (Br) = number of independent samples that
are averaged
Setting SIN equal to unity we find for the received
signal-to-noise
ratio
Pr 1 +x/rl-+ n
-- = (8)
Po
n
We use equation (119) in estimating range limits when
the data processing system is unspecified. However, in
determining the performance of the Cyclops system we
use the actual range limit at which the probability of
missing the signal Pros and the probability of a false
alarm Pfa have specified values. That is, we take
draper f -- q ,/2
R = -- f(n,Pms,Pr,) I (11)
4_--_
where f(n,Pms,Pfq) is evaluated for the proposed data
processing method using the actual statistics, and will be
a number on the order of unity. Anticipating this, we
will use as a reference range limit for some of our curves
the range Ro
given by
/ \I/2
dr(Peff.
4\/
which is simply the range at which the received
signal-to-noise ratio is unity and is less than R, as given
by equation (9), for n > 3.
DOPPLER SHIFTS AND RATES
Relative motion between transmitter and receiver can
occur because of (1) radial velocity of the star with respect
to the Sun, (2) orbital velocity of the Earth and
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